A Family of Fast Spherical Registration Algorithms for Cortical Shapes

We introduce a family of fast spherical registration algorithms: a spherical fluid model and several modifications of the spherical demons algorithm introduced in [1]. Our algorithms are based on fast convolution of tangential spherical vector fields in the spectral domain. Using the vector harmonic representation of spherical fields, we derive a more principled approach for kernel smoothing via Mercer’s theorem and the diffusion equation. This is a non-trivial extension of scalar spherical convolution, as the vector harmonics do not generalize directly from scalar harmonics on the sphere, as in the Euclidean case. The fluid algorithm is optimized in the Eulerian frame, leading to a very efficient optimization. Several new adaptations of the demons algorithm are presented, including compositive and diffeomorphic demons, as well as fluid-like and diffusion-like regularization. The resulting algorithms are all significantly faster than [1], while also retaining greater flexibility. Our algorithms are validated and compared using cortical surface models.